INTRODUCTION
My last few posts have described a new method for quantifying the average Urban Heat Island (UHI) warming effect as a function of population density, using thousands of pairs of temperature measuring stations within 150 km of each other. The results supported previous work which had shown that UHI warming increases logarithmically with population, with the greatest rate of warming occurring at the lowest population densities as population density increases.

But how does this help us determine whether global warming trends have been spuriously inflated by such effects remaining in the leading surface temperature datasets, like those produced by Phil Jones (CRU) and Jim Hansen (NASA/GISS)?

While my quantifying the UHI effect is an interesting exercise, the existence of such an effect spatially (with distance between stations) does not necessarily prove that there has been a spurious warming in the thermometer measurements at those stations over time. The reason why it doesn’t is that, to the extent that the population density of each thermometer site does not change over time, then various levels of UHI contamination at different thermometer sites would probably have little influence on long-term temperature trends. Urbanized locations would indeed be warmer on average, but “global warming” would affect them in about the same way as the more rural locations.

This hypothetical situation seems unlikely, though, since population does indeed increase over time. If we had sufficient truly-rural stations to rely on, we could just throw all the other UHI-contaminated data away. Unfortunately, there are very few long-term records from thermometers that have not experienced some sort of change in their exposure…usually the addition of manmade structures and surfaces that lead to spurious warming.

Thus, we are forced to use data from sites with at least some level of UHI contamination. So the question becomes, how does one adjust for such effects?

As the provider of the officially-blessed GHCN temperature dataset that both Hansen and Jones depend upon, NOAA has chosen a rather painstaking approach where the long-term temperature records from individual thermometer sites have undergone homogeneity “corrections” to their data, mainly based upon (presumably spurious) abrupt temperature changes over time. The coming and going of some stations over the years further complicates the construction of temperature records back 100 years or more.

All of these problems (among others) have led to a hodgepodge of complex adjustments.

A SIMPLER TECHNIQUE TO LOOK FOR SPURIOUS WARMING

I like simplicity of analysis — whenever possible, anyway. Complexity in data analysis should only be added when it is required to elucidate something that is not obvious from a simpler analysis. And it turns out that a simple analysis of publicly available raw (not adjusted) temperature data from NOAA/NESDIS NOAA/NCDC, combined with high-resolution population density data for those temperature monitoring sites, shows clear evidence of UHI warming contaminating the GHCN data for the United States.

I will restrict the analysis to 1973 and later since (1) this is the primary period of warming allegedly due to anthropogenic greenhouse gas emissions; (2) the period having the largest number of monitoring sites has been since 1973; and (3) a relatively short 37-year record maximizes the number of continuously operating stations, avoiding the need to handle transitions as older stations stop operating and newer ones are added.

Similar to my previous posts, for each U.S. station I average together four temperature measurements per day (00, 06, 12, and 18 UTC) to get a daily average temperature (GHCN uses daily max/min data). There must be at least 20 days of such data for a monthly average to be computed. I then include only those stations having at least 90% complete monthly data from 1973 through 2009. Annual cycles in temperature and anomalies are computed from each station separately.

I then compute multi-station average anomalies in 5×5 deg. latitude/longitude boxes, and then compare the temperature trends for the represented regions to those in the CRUTem3 (Phil Jones’) dataset for the same regions. But to determine whether the CRUTem3 dataset has any spurious trends, I further divide my averages into 4 population density classes: 0 to 25; 25 to 100; 100 to 400; and greater than 400 persons per sq. km. The population density data is at a nominal 1 km resolution, available for 1990 and 2000…I use the 2000 data.

All of these restrictions then result in thirteen 24 to 26 5-deg grid boxes over the U.S. having all population classes represented over the 37-year period of record. In comparison, the entire U.S. covers about 31 40 grid boxes in the CRUTem3 dataset. While the following results are therefore for a regional subset (at least 60%) of the U.S., we will see that the CRUTem3 temperature variations for the entire U.S. do not change substantially when all 31 40 grids are included in the CRUTem3 averaging.

EVIDENCE OF A LARGE SPURIOUS WARMING TREND IN THE U.S. GHCN DATA

The following chart shows yearly area-averaged temperature anomalies from 1973 through 2009 for the 13 24 to 26 5-deg. grid squares over the U.S. having all four population classes represented (as well as a CRUTem3 average temperature measurement). All anomalies have been recomputed relative to the 30-year period, 1973-2002.

The heavy red line is from the CRUTem3 dataset, and so might be considered one of the “official” estimates. The heavy blue curve is the lowest population class. (The other 3 population classes clutter the figure too much to show, but we will soon see those results in a more useful form.)

Significantly, the warming trend in the lowest population class is only 47% of the CRUTem3 trend, a factor of two difference.

Also interesting is that in the CRUTem3 data, 1998 and 2006 would be the two warmest years during this period of record. But in the lowest population class data, the two warmest years are 1987 and 1990. When the CRUTem3 data for the whole U.S. are analyzed (the lighter red line) the two warmest years are swapped, 2006 is 1st and then 1998 2nd.

From looking at the warmest years in the CRUTem3 data, one gets the impression that each new high-temperature year supersedes the previous one in intensity. But the low-population stations show just the opposite: the intensity of the warmest years is actually decreasing over time.

To get a better idea of how the calculated warming trend depends upon population density for all 4 classes, the following graph shows – just like the spatial UHI effect on temperatures I have previously reported on – that the warming trend goes down nonlinearly as population density of the stations decrease. In fact, extrapolation of these results to zero population density might produce little warming at all!

This is a very significant result. It suggests the possibility that there has been essentially no warming in the U.S. since the 1970s.

Also, note that the highest population class actually exhibits slightly more warming than that seen in the CRUTem3 dataset. This provides additional confidence that the effects demonstrated here are real.

Finally, the next graph shows the difference between the lowest population density class results seen in the first graph above. This provides a better idea of which years contribute to the large difference in warming trends.

Taken together, I believe these results provide powerful and direct evidence that the GHCN data still has a substantial spurious warming component, at least for the period (since 1973) and region (U.S.) addressed here.

There is a clear need for new, independent analyses of the global temperature data…the raw data, that is. As I have mentioned before, we need independent groups doing new and independent global temperature analyses — not international committees of Nobel laureates passing down opinions on tablets of stone.

But, as always, the analysis presented above is meant more for stimulating thought and discussion, and does not equal a peer-reviewed paper. Caveat emptor.

My post from yesterday showed a rather unexpected difference between the United States versus the rest of the world for the average urban heat island (UHI) temperature-population relationship. Updated results shown below have now reduced that discrepancy…but not removed it.

I have now included more station temperature and population data by removing my requirement that two neighboring temperature measurement stations must have similar fractions of water coverage (lakes, coastlines, etc.). The results (shown below, second panel) reveal less of a discrepancy between the U.S. and the rest of the world than in my previous post. The US now shows weak warming at the lowest population densities, rather than cooling as was presented yesterday.

Also, I adjusted the population bin boundaries used for averaging to provide more uniform numbers of station pairs per bin. This has reduced the differences between individual years (top panel), suggesting more robust results. It has also increased the overall UHI warming effect, with about 1.0 deg. C average warming at a population density of 100 persons per sq. km.

This is an update to my previous post describing a new technique for estimating the average amount of urban heat island (UHI) warming accompanying an increase in population density. The analysis is based upon 4x per day temperature observations in the NOAA International Surface Hourly (ISH) dataset, and on 1 km population density data for the year 2000.

I’m providing a couple of charts with new results, below. The first chart shows the global yearly average warming-vs-population density increase from each year from 2000 to 2009. They all show clear evidence of UHI warming, even for small population density increases at very low population density. A population density of only 100 persons per sq. km exhibits average warming of about 0.8 deg. C compared to a nearby unpopulated temperature monitoring location.

In this analysis, the number of independent temperature monitoring stations having at least 1 neighboring station with a lower population density within 150 km of it, increased from 2,183 in 2000, to 4,290 in 2009…an increase by a factor of 2 in ten years. The number of all resulting station pairs increased from 9,832 in 2000 to 30,761 in 2009, an increase of 3X.

The next chart shows how the results for the U.S. differ from non-US stations. In order to beat down the noise for the US-only results, I included all ten years (2000 thru 2009) in the analysis. The US results are obviously different from the non-US stations, with much less warming with an increase in population density, and even evidence of an actual slight cooling for the lowest population categories.

The cooling signal appeared in 5 of the 10 years, not all of them, a fact I am mentioning just in case someone asks whether it existed in all 10 years. I don’t know the reason for this, but I suspect that a little thought from Anthony Watts, Joe D’Aleo & others will help figure it out.

John Christy has agreed to co-author a paper on this new technique, since he has some experience publishing in this area of research (UHI & land use change effects on thermometer data) than me. We have not yet decided what journal to submit to.

UPDATED: 2:16 p.m. CST March 6, 2010: Added a plot of the differences between v5.3 and v5.2.

YR MON GLOBE NH SH TROPICS
2009 1 0.213 0.418 0.009 -0.119
2009 2 0.220 0.557 -0.117 -0.091
2009 3 0.174 0.335 0.013 -0.198
2009 4 0.135 0.290 -0.020 -0.013
2009 5 0.102 0.109 0.094 -0.112
2009 6 0.022 -0.039 0.084 0.074
2009 7 0.414 0.188 0.640 0.479
2009 8 0.245 0.243 0.247 0.426
2009 9 0.502 0.571 0.433 0.596
2009 10 0.353 0.295 0.410 0.374
2009 11 0.504 0.443 0.565 0.482
2009 12 0.262 0.331 0.190 0.482
2010 1 0.630 0.809 0.451 0.677
2010 2 0.613 0.720 0.506 0.789

The global-average lower tropospheric temperature remained high, at +0.61 deg. C for February, 2010. This is about the same as January, which in our new Version 5.3 of the UAH dataset was +0.63 deg. C. February was second warmest in the 32-year record, behind Feb 1998 which was itself the second warmest of all months. The El Nino is still the dominant temperature signal; many people living in Northern Hemisphere temperate zones were still experiencing colder than average weather.

The new dataset version does not change the long-term trend in the dataset, nor does it yield revised record months; it does, however, reduce some of the month-to-month variability, which has been slowly increasing over time.

Version 5.3 accounts for the mismatch between the average seasonal cycle produced by the older MSU and the newer AMSU instruments. This affects the value of the individual monthly departures, but does not affect the year to year variations, and thus the overall trend remains the same.

Here is a comparison of v5.2 and v5.3 for global anomalies in lower tropospheric temperature.

YR MON v5.2 v5.3
2009 1 0.304 0.213
2009 2 0.347 0.220
2009 3 0.206 0.174
2009 4 0.090 0.135
2009 5 0.045 0.102
2009 6 0.003 0.022
2009 7 0.411 0.414
2009 8 0.229 0.245
2009 9 0.422 0.502
2009 10 0.286 0.353
2009 11 0.497 0.504
2009 12 0.288 0.262
2010 1 0.721 0.630
2010 2 0.740 0.613

trends since 11/78: +0.132 +0.132 deg. C per decade

The following discussion is provided by John Christy:
As discussed in our running technical comments last July, we have been looking at making an adjustment to the way the average seasonal cycle is removed from the newer AMSU instruments (since 1998) versus the older MSU instruments. At that time, others (e.g. Anthony Watts) brought to our attention the fact that UAH data tended to have some systematic peculiarities with specific months, e.g. February tended to be relatively warmer while September was relatively cooler in these comparisons with other datasets. In v5.2 of our dataset we relied considerably on the older MSUs to construct the average seasonal cycle used to calculated the monthly departures for the AMSU instruments. This created the peculiarities noted above. In v5.3 we have now limited this influence.

UPDATE: The following chart, which differences the v5.3 and v5.2 versions of the dataset clearly illustrates this spurious component to the seasonal cycle which has been removed:
TLT_GL_v.5.2_vs_v5.3

The adjustments are very minor in terms of climate as they impact the relative departures within the year, not the year-to-year variations. Since the errors are largest in February (almost 0.13 C), we believe that February is the appropriate month to introduce v5.3 where readers will see the differences most clearly. Note that there is no change in the long term trend as both v5.2 and v5.3 show +0.132 C/decade. All that happens is a redistribution of a fraction of the anomalies among the months. Indeed, with v5.3 as with v5.2, Jan 2010 is still the warmest January and February 2010 is the second warmest Feb behind Feb 1998 in the 32-year record.

For a more detailed discussion of this issue written last July, email John Christy at christy@nsstc.uah.edu for the document.

[NOTE: These satellite measurements are not calibrated to surface thermometer data in any way, but instead use on-board redundant precision platinum resistance thermometers (PRTs) carried on the satellite radiometers. The PRT’s are individually calibrated in a laboratory before being installed in the instruments.]

UPDATE #1 (12:30 p.m. CST, March 3): Appended new discussion & plots showing importance of how low-population density stations are handled.

UPDATE #2 (9:10 a.m. CST, March 4): Clarifications on methodology and answers to questions.

ABSTRACT
Global hourly surface temperature observations and 1 km resolution population density data for the year 2000 are used together to quantify the average urban heat island (UHI) effect. While the rate of warming with population increase is the greatest at the lowest population densities, some warming continues with population increases even for densely populated cities. Statistics like those presented here could be used to correct the surface temperature record for spurious warming caused by the UHI effect, providing better estimates of temperature trends.

METHOD
Using NOAA’s International Surface Hourly (ISH) weather data from around the world during 2000, I computed daily, monthly, and then 1-year average temperatures for each weather station. For a station to be used, a daily average temperature computation required the 4 synoptic temperature observations at 00, 06, 12, and 18 UTC; a monthly average required at least 20 good days per month; and a yearly average required all 12 months.

For each of those weather station locations I also stored the average population density from the 1 km gridded global population density data archived at the Socioeconomic Data and Applications Center (SEDAC).

All station pairs within 150 km of each other had their 1-year average difference in temperature related to their difference in population. Averaging of these station pairs’ results was done in 10 population bins each for Station1 and Station2, with bin boundaries at 0, 20, 50, 100, 200, 400, 800, 1600, 3200, 6400, and 50000 persons per sq. km.

Because some stations are located next to large water bodies, I used an old USAF 1/6 deg lat/lon percent water coverage dataset to ensure that there was no more than a 20% difference in the percent water coverage between the two stations in each match-up. (I believe this water coverage dataset is no longer publicly available).

Elevation effects were estimated by regressing station pair temperature differences against station elevation differences, which yielded a cooling rate of 5.4 deg. C per km increase in station elevation. Then, all station temperatures were adjusted to sea level (0 km elevation) with this relationship.

After all screening, a total of 10,307 unique station pairs were accepted for analysis from 2000.

RESULTS & DISCUSSION
The following graph shows the average rate of warming with population density increase (vertical axis), as a function of the average populations of the station pairs. Each data point represents a population bin average for the intersection of a higher population station with its lower-population station mate.

Using the data in the above graph, we can now compute average cumulative warming from a population density of zero, the results of which are shown in the next graph. [Note that this step would be unnecessary if every populated station location had a zero-population station nearby. In that case, it would be much easier to compute the average warming associated with a population density increase.]

This graph shows that the most rapid rate of warming with population increase is at the lowest population densities. The non-linear relationship is not a new discovery, as it has been noted by previous researchers who found an approximate logarithmic dependence of warming on population.

Significantly, this means that monitoring long-term warming at more rural stations could have greater spurious warming than monitoring in the cities. For instance, a population increase from 0 to 20 people per sq. km gives a warming of +0.22 deg C, but for a densely populated location having 1,000 people per sq. km, it takes an additional 1,500 people (to 2,500 people per sq. km) to get the same 0.22 deg. C warming. (Of course, if one can find stations whose environment has not changed at all, that would be the preferred situation.)

Since this analysis used only 1 year of data, other years could be examined to see how robust the above relationship is. Also, since there are gridded population data for 1990, 2000, and 2010 (estimated), one could examine whether there is any indication of the temperature-population relationship changing over time.

This is the type of information which I can envision being used to adjust station temperatures throughout the historical record, even as stations come, go, and move. As mentioned above, the elevation adjustment for individual stations can be done fairly easily, and the population adjustments could then be done without having to inter-calibrate stations.

Such adjustments help to maximize the number of stations used in temperature trend analysis, rather than simply throwing the data out. Note that the philosophy here is not to provide the best adjustments for each station individually, but to do adjustments for spurious effects which, when averaged over all stations, will remove the effect when averaged over all stations. This ensures simplicity and reproducibility of the analysis.

UPDATE #1:
The above results are quite sensitive to how the stations with very low population densities are handled. I’ve recomputed the above results by adding a single data point representing 724 more station pairs where BOTH stations are within the lowest population density category: 0 to 20 people per sq. km. This increases the signal of warming at low population densities, from the previously mentioned +0.22 deg C warming from zero to 20 people per sq. km, to +0.77 deg. C of warming.

This is over a factor of 3 more warming from 0 to 20 persons per sq. km with the additional data. This is important because most weather observation sites have relatively low population densities: in my dataset, I find that one-half of all stations have population densities below 100 persons per sq. km. The following plot zooms in on the lower left corner of the previous plot so you can better see the warming at the lowest population densities.

Clearly, any UHI adjustments to past thermometer data will depend upon how the UHI effect is quantified at these very low population densities.

Also, since I didn’t mention it earlier, I should clarify that population density is just an accessible index that is presumed to be related to how much the environment around the thermometer site has been modified over time, by replacing vegetation with manmade structures. Population density is not expected to always be a good index of this modification — for instance, population densities at large airports can be expected to be low, but the surrounding runway surfaces and airplane traffic can be expected to cause considerable spurious warming, much more than would be expected for their population density.

UPDATE #2: Clarifications and answers to questions

After sifting through the 212 comments posted in the last 12 hours at Anthony Watts’ site, I thought I would answer those concerns that seemed most relevant.

Many of the questions and objections posted there were actually answered by others peoples’ posts — see especially the 2 comments by Jim Clarke at time stamps 18:23:56 & 01:32:40. Clearly, Jim understood what I did, why I did it, and phrased the explanations even better than I could have.

Some readers were left confused since my posting was necessarily greatly simplified; the level of detail for a journal submission would increase by about a factor of ten. I appreciate all the input, which has helped clarify my thinking.

RATIONALE FOR THE STUDY

While it might not have been obvious, I am trying to come up with a quantitative method for correcting past temperature measurements for the localized warming effects due to the urban heat island (UHI) effect. I am generally including in the “UHI effect” any replacement of natural vegetation by manmade surfaces, structures and active sources of heat. I don’t want to argue about terminology, just keep things simple.

For instance, the addition of an outbuilding and a sidewalk next to an otherwise naturally-vegetated thermometer site would be considered UHI-contaminated. (As Roger Pielke, Sr., has repeatedly pointed out, changes in land use, without the addition of manmade surfaces and structures, can also cause temperature changes. I consider this to be a much more difficult influence to correct for in the global thermometer data.)

The UHI effect leads to a spurious warming signal which, even though only local, has been given global significance by some experts. Many of us believe that as much as 50% (or more) of the “global warming” signal in the thermometer data could actually be from local UHI effects. The IPCC community, in contrast, appears to believe that the thermometer record has not been substantially contaminated.

Unless someone quantitatively demonstrates that there is a significant UHI signal in the global thermometer data, the IPCC can claim that global temperature trends are not substantially contaminated by such effects.

If there were sufficient thermometer data scattered around the world that are unaffected by UHI effects, then we could simply throw away all of the contaminated data. A couple of people wondered why this is not done. I believe that there is not enough uncontaminated data to do this, which means we must find some way of correcting for UHI effects that exist in most of the thermometer data — preferably extending back 100 years or more.

Since population data is one of the few pieces of information that we have long term records for, it makes sense to determine if we can quantify the UHI effect based upon population data. My post introduces a simple method for doing that, based upon the analysis of global thermometer and population density data for a single year, 2000. The analysis needs to be done for other years as well, but the high-resolution population density data only extends back to 1990.

Admittedly, if we had good long-term records of some other variable that was more closely related to UHI, then we could use that instead. But the purpose here is not to find the best way to estimate the magnitude of TODAY’S UHI effect, but to find a practical way to correct PAST thermometer data. What I posted was the first step in that direction.

Clearly, satellite surveys of land use change in the last 10 or 20 years are not going to allow you to extend a method back to 1900. Population data, though, ARE available (although of arguable quality). But no method will be perfect, and all possible methods should be investigated.

STATION PAIRING

My goal is to quantify how much of a UHI temperature rise occurs, on average, for any population density, compared to a population density of zero. We can not do this directly because that would require a zero-population temperature measurement near every populated temperature measurement location. So, we must do it in a piecewise fashion.

For every closely-spaced station pair in the world, we can compare the temperature difference between the 2 stations to the population density difference between the two station locations. Using station pairs is easily programmable on a computer, allowing the approx 10,000 temperature measurements sites to be processed relatively quickly.

Using a simple example to introduce the concept, theoretically one could compute:

1) how much average UHI warming occurs from going from 0 to 20 people per sq. km, then
2) the average warming going from 20 to 50 people per sq. km, then
3) the average warming going from 50 to 100 people per. sq. km,
etc.

If you can compute all of these separate statistics, we can determine how the UHI effect varies with population density going from 0 to the highest population densities.

Unfortunately, the populations of any 2 closely-spaced stations will be highly variable, not neatly ordered like this simple example. We need some way of handling the fact that stations do NOT have population densities exactly at 0, 20, 100 (etc.) persons per sq. km., but can have ANY population density. I handle this problem by doing averaging in specific population intervals.

For each pair of closely spaced stations, if the higher-population station is in population interval #3, and the lower population station is in population interval #1, I put that station pair’s year-average temperature difference in a 2-dimensional (interval#3, interval#1) population “bin” for later averaging.

Not only is the average temperature difference computed for all station pairs falling in each population bin, but also computed are the average populations in those bins. We will need those statistics later for our calculations of how temperature increases with population density.

Note that we can even compute the temperature difference between stations in the SAME population bin, as long as we keep track of which one has the higher population and which has the lower population. If the population densities for a pair of stations are exactly the same, we do not include that pair in the averaging.

The fact that the greatest warming RATE is observed at the lowest population densities is not a new finding. My comment that the greatest amount of spurious warming might therefore occur at the rural (rather than urban) sites, as a couple of people pointed out, presumes that rural sites tend to increase in population over the years. This might not be the case for most rural sites.

Also, as some pointed out, the UHI warming will vary with time of day, season, geography, wind conditions, etc. These are all mixed in together in my averages. But the fact that a UHI signal clearly exists without any correction for these other effects means that the global warming over the last 100 years measured using daily max/min temperature data has likely been overestimated. This is an important starting point, and its large-scale, big-picture approach complements the kind of individual-station surveys that Anthony Watts has been performing.